Turbine Nozzle Airfoil Profile

ABSTRACT

The present application provides a turbine nozzle including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances may be joined smoothly with one another to form a complete airfoil shape.

FIELD

The present application relates generally to a turbine nozzle for a gas turbine engine, and more particularly relates to a turbine nozzle airfoil profile for a turbine nozzle.

BACKGROUND

Some aircraft and/or power plant systems, for example certain jet aircraft, nuclear, simple cycle and combined cycle power plant systems, employ turbines (also referred to as turbomachines) in their design and operation. Some of these turbines employ airfoils (e.g., stator vanes or nozzles and rotor blades) which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and generate energy (e.g., creating thrust, turning kinetic energy to mechanical energy, converting thermal energy to mechanical energy, etc.) from these fluid flows as part of power generation. As a result of this interaction and conversion, the aerodynamic characteristics and losses of these airfoils have an impact on system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION

Aspects and advantages of the turbines and turbine nozzles in accordance with the present disclosure will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the technology.

In accordance with one embodiment, the present application provides a turbine nozzle including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances may be joined smoothly with one another to form a complete airfoil shape.

In accordance with another embodiment, the present application provides a turbine nozzle including an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance. The airfoil profile sections at the Z distances may be joined smoothly with one another to form a complete (uncoated) suction-side airfoil shape. The X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.

In accordance with another embodiment, the present application provides a turbine with a plurality of turbine nozzles, each having an airfoil having an airfoil shape. The airfoils each have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance. The airfoil profile sections at the Z distances may be joined smoothly with one another to form a complete airfoil shape.

These and other features, aspects and advantages of the present turbines and turbine nozzles will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the technology and, together with the description, serve to explain the principles of the technology.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present turbines and turbine nozzles, including the best mode of making and using the present systems and methods, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which:

FIG. 1 is a schematic representation of an exemplary turbine having multiple stages with each stage including, in alternating relationship, a row of turbine rotor blades and a row of turbine nozzles, according to at least one embodiment of the present disclosure;

FIG. 2 is a perspective view of an exemplary turbine nozzle according to at least one embodiment of the present disclosure; and

FIG. 3 provides a cross-sectional view of an airfoil portion of the turbine nozzle of FIG. 2.

DETAILED DESCRIPTION

Reference now will be made in detail to embodiments of the present turbines and turbine nozzles, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation, rather than limitation of, the technology. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present technology without departing from the scope or spirit of the claimed technology. For instance, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present disclosure covers such modifications and variations as come within the scope of the appended claims and their equivalents.

The detailed description uses numerical and letter designations to refer to features in the drawings. Like or similar designations in the drawings and description have been used to refer to like or similar parts of the invention. As used herein, the terms “first”, “second”, and “third” may be used interchangeably to distinguish one component from another and are not intended to signify location or importance of the individual components.

Referring now to the drawings, particularly to FIG. 1, there is illustrated an exemplary turbine 10 of a gas turbine 12 including a plurality of turbine stages arranged in serial flow order. Each stage of the turbine includes a row of stationary turbine nozzles or vanes disposed axially adjacent to a corresponding row of rotating turbine rotor blades. Four stages are illustrated in FIG. 1. The exact number of stages of the turbine 10 is a choice of engineering design and may be more or less than the four stages illustrated in FIG. 1. The four stages are merely exemplary of one turbine design and are not intended to limit the presently claimed turbine rotor blade in any manner.

The first stage comprises a plurality of turbine nozzles or vanes 100 and a plurality of turbine rotor blades 150. The turbine nozzles 100 are annularly arranged about an axis of a turbine rotor 14. The turbine rotor blades 150 are annularly arranged about and coupled to the turbine rotor 14. A second stage of the turbine 12 includes a plurality of turbine nozzles 200 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 250 annularly arranged about and coupled to the turbine rotor 14. The turbine nozzles 200 may be coupled to a casing 10 of the turbine 12.

As shown in FIG. 1, a third stage of the turbine 12 includes a plurality of turbine nozzles 300 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 350 annularly arranged about and coupled to the turbine rotor 14. The turbine nozzles 300 may be coupled to the casing 10 of the turbine 12. In particular embodiments, the turbine 12 includes a fourth stage, which includes plurality of turbine nozzles 400 annularly arranged about the axis of the turbine rotor 14 and a plurality of turbine rotor blades 450 annularly arranged about and coupled to the turbine rotor 14. The fourth stage turbine nozzles 400 may be coupled to the casing 10 of the turbine 12.

It will be appreciated that the turbine nozzles 100, 200, 300 and 400 and turbine rotor blades 150, 250, 350 and 450 are disposed or at least partially disposed within a hot gas path 18 of the turbine 12. The various stages of the turbine 12 at least partially define the hot gas path 18 through which combustion gases, as indicated by arrows 20, flow during operation of the gas turbine 12.

FIG. 2 provides a perspective view of an exemplary turbine nozzle 50 as may be incorporated in any stage of the turbine 12. FIG. 3 provides a cross-sectional top view of an airfoil 52 of the turbine nozzle 50 shown in FIG. 2. In one embodiment, the turbine nozzle 50 as provided in Table I below is representative of one or more turbine nozzles 100 of the plurality of turbine nozzles 100 of the first stage as shown in FIG. 1. As shown in FIGS. 2 and 3 collectively, the turbine nozzle 50 airfoil 52 includes a pressure-side wall 54 and an opposing suction-side wall 56. The pressure-side wall 54 and the suction-side wall 56 meet or intersect at a leading edge 58 and at a trailing edge 60 of the airfoil 52. A chord line 62 extends between the leading edge 58 and the trailing edge 60 such that pressure- and suction-side walls 54, 56 can be said to extend in chord or chordwise between the leading edge 58 and the trailing edge 60.

As shown in FIG. 2, the airfoil 52 includes a root or first end 64, which intersects with and extends radially outwardly from an inner band 66 of the turbine nozzle 50. The airfoil 52 terminates radially at a second end or tip 68 of the airfoil 52. The second end 68 intersects with and extends radially inwardly from an outer band 70 of the turbine nozzle 50. The pressure- and suction-side walls 54, 56 can be said to extend in height and/or span or in a span-wise direction 72 between the root 64 and/or the inner band 66 and the second end 68 or the outer band 70. In other words, each turbine nozzle 50 includes an airfoil 52 having opposing pressure- and suction-side walls 54, 56 that extend in chord or chordwise 62 between opposing leading and trailing edges 58, 60 and that extend in span or span-wise direction 72 between the root 64 and the second end 68 of the airfoil 52.

In particular configurations, the airfoil 52 may include a fillet 74 formed between the inner band 66 and the airfoil 52 proximate to the root 64. The fillet 74 can include a weld or braze fillet, which can be formed via conventional MIG welding, TIG welding, brazing, etc., and can include a profile that can reduce fluid dynamic losses as a result of the presence of fillet 74. In particular embodiments, the inner band 66, airfoil 52 and the fillet 74 can be formed as a single component, such as by casting and/or machining and/or 3D printing and/or any other suitable technique now known or later developed and/or discovered.

The airfoil 52 of the turbine nozzle 50 has a profile at any cross-section taken between the inner band 66 or the root 64 and the second end 68. The X, Y, and Z values are given in Table I as percentage values of the airfoil length or height/span. As one example only, the height or radial span of the airfoil 52 of turbine nozzle 50 may be from about 2 inches to about 50 inches (about 5 centimeters to about 130 centimeters). However, it is to be understood that heights below or above this range may also be employed as desired in the specific application.

The gas turbine hot gas path 18 requires airfoils 52 that meet system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each turbine nozzle airfoil 52, there is a unique set or loci of points in space that meet the stage requirements and that can be manufactured. These unique loci of points meet the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system.

The loci that defines the turbine nozzle airfoil profile includes a set of about 2,200 points with X, Y and Z dimensions relative to a reference origin coordinate system. The Cartesian coordinate system of X, Y and Z values given in Table I below defines the profile of the turbine nozzle airfoil at various locations along its height. Table I lists data for a non-coated airfoil. The envelope/tolerance for the coordinates is about +/−5% in a direction normal to any airfoil surface location and/or about +/−5% of the chord 62 in a direction nominal to any airfoil surface location. The point data origin 76 is defined at or proximate to the leading edge 58 of the airfoil 52 and at or proximate to the root 64.

The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units by the values provided in Table I, although other units of dimensions may be used when the values are appropriately converted. The X, Y and Z values set forth in Table I are also expressed in non-dimensional form (X, Y, and Z) from 0% to 100% of the height or span of the airfoil 52. As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the leading edge 58 and multiplying by a constant number (e.g., 100). As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the trailing edge 60 and multiplying by a constant number (e.g., 100).

To convert the Z value to a Z coordinate value, e.g., in inches, the non-dimensional Z value given in Table I is multiplied by the Z height of the airfoil in inches. As described above, the Cartesian coordinate system has orthogonally-related X, Y and Z axes, and the X axis lies generally parallel to the turbine rotor centerline, i.e., the rotary axis, and a positive X coordinate value is axial toward an exhaust end of the turbine 14. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor shaft 14, and the positive Z coordinate value is radially outwardly toward the second end 68 of the airfoil 52. All the values in Table I are given at room temperature and are non-filleted.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section or airfoil shape of the airfoil 52 of the turbine nozzle 50, at each Z distance along the height of the airfoil 52 can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each distance Z is fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table I values are generated and shown to four decimal places for determining the profile of the airfoil. As the turbine nozzle surface heats up during operation of the turbine 14, mechanical stresses and elevated temperatures will cause a change in the X, Y and Z values. Accordingly, the values for the profile given in Table I represent the profile of an uncoated airfoil at ambient, non-operating or non-hot conditions (e.g., room temperature).

There are typical manufacturing tolerances as well as coatings that must be accounted for in the actual profile of the airfoil 52. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of +/−5% in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular turbine nozzle airfoil design and turbine, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the Table below at the same temperature. The data is scalable (i.e., by uniform geometric scaling), and the geometry pertains to all aerodynamic scales, at above and/or below 3000 RPM. The design of the airfoil 52 of the turbine nozzle 50 is robust to this range of variation without impairment of mechanical and aerodynamic functions.

TABLE I SUCTION-SIDE PRESSURE-SIDE X (%) Y (%) Z (%) X (%) Y (%) Z (%) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7518 −2.6977 0.0000 −0.3351 2.1779 0.0000 1.8343 −5.2537 0.0000 −0.4382 4.3644 0.0000 3.2562 −7.6593 0.0000 −0.3050 6.5596 0.0000 4.9658 −9.8673 0.0000 0.0601 8.7418 0.0000 6.9161 −11.8562 0.0000 0.6272 10.8682 0.0000 9.0940 −13.6088 0.0000 1.3875 12.9344 0.0000 11.4309 −15.1252 0.0000 2.3412 14.9233 0.0000 13.8666 −16.4182 0.0000 3.4795 16.7963 0.0000 16.3839 −17.5265 0.0000 4.7640 18.5618 0.0000 18.9742 −18.4845 0.0000 6.1472 20.2586 0.0000 21.6203 −19.3092 0.0000 7.5948 21.9039 0.0000 24.3095 −20.0052 0.0000 9.0854 23.5191 0.0000 27.0244 −20.5636 0.0000 10.5975 25.1085 0.0000 29.7521 −20.9674 0.0000 12.1225 26.6893 0.0000 32.5014 −21.1994 0.0000 13.6561 28.2572 0.0000 35.2807 −21.2380 0.0000 15.1982 29.8209 0.0000 38.0601 −21.0576 0.0000 16.7404 31.3759 0.0000 40.7964 −20.6409 0.0000 18.2912 32.9267 0.0000 43.4770 −19.9751 0.0000 19.8462 34.4731 0.0000 46.1016 −19.0472 0.0000 21.4056 36.0153 0.0000 48.6275 −17.8745 0.0000 22.9692 37.5532 0.0000 51.0116 −16.4741 0.0000 24.5371 39.0867 0.0000 53.2669 −14.8675 0.0000 26.1094 40.6160 0.0000 55.4019 −13.0805 0.0000 27.6859 42.1410 0.0000 57.4037 −11.1474 0.0000 29.2667 43.6660 0.0000 59.2723 −9.1112 0.0000 30.8475 45.1866 0.0000 61.0293 −6.9805 0.0000 32.4284 46.7073 0.0000 62.6874 −4.7682 0.0000 34.0092 48.2323 0.0000 64.2682 −2.4829 0.0000 35.5857 49.7530 0.0000 65.7674 −0.1504 0.0000 37.1622 51.2823 0.0000 67.1936 2.2209 0.0000 38.7302 52.8115 0.0000 68.5511 4.6179 0.0000 40.2938 54.3494 0.0000 69.8484 7.0364 0.0000 41.8489 55.8959 0.0000 71.0941 9.4806 0.0000 43.3953 57.4423 0.0000 72.2926 11.9378 0.0000 44.9332 59.0017 0.0000 73.4439 14.4164 0.0000 46.4625 60.5653 0.0000 74.5651 16.9079 0.0000 47.9832 62.1375 0.0000 75.6519 19.4081 0.0000 49.4953 63.7141 0.0000 76.7129 21.9253 0.0000 50.9945 65.2992 0.0000 77.7482 24.4469 0.0000 52.4808 66.8929 0.0000 78.7577 26.9814 0.0000 53.9542 68.4995 0.0000 79.7457 29.5245 0.0000 55.4190 70.1147 0.0000 80.7165 32.0761 0.0000 56.8667 71.7385 0.0000 81.6659 34.6364 0.0000 58.2972 73.3751 0.0000 82.5980 37.2009 0.0000 59.7148 75.0204 0.0000 83.5130 39.7697 0.0000 61.1195 76.6828 0.0000 84.4108 42.3515 0.0000 62.5027 78.3539 0.0000 85.2958 44.9332 0.0000 63.8730 80.0378 0.0000 86.1678 47.5235 0.0000 65.2305 81.7346 0.0000 87.0226 50.1181 0.0000 66.5664 83.4443 0.0000 87.8646 52.7213 0.0000 67.8895 85.1669 0.0000 88.6980 55.3245 0.0000 69.1911 86.8981 0.0000 89.5142 57.9363 0.0000 70.4798 88.6464 0.0000 90.3217 60.5481 0.0000 71.7514 90.4034 0.0000 91.1208 63.1685 0.0000 73.0057 92.1775 0.0000 91.9069 65.7932 0.0000 74.2429 93.9602 0.0000 92.6801 68.4179 0.0000 75.4672 95.7601 0.0000 93.4447 71.0512 0.0000 76.6743 97.5686 0.0000 94.2008 73.6844 0.0000 77.8642 99.3900 0.0000 94.9396 76.3177 0.0000 79.0369 101.2243 0.0000 95.6742 78.9596 0.0000 80.1924 103.0671 0.0000 96.3916 81.6014 0.0000 81.3351 104.9272 0.0000 97.1004 84.2433 0.0000 82.4606 106.7958 0.0000 97.8006 86.8895 0.0000 83.5646 108.6816 0.0000 98.4879 89.5399 0.0000 84.6557 110.5761 0.0000 99.1623 92.1904 0.0000 85.7339 112.4834 0.0000 99.8239 94.8451 0.0000 86.7950 114.4035 0.0000 100.4768 97.5042 0.0000 87.8431 116.3323 0.0000 101.1169 100.1632 0.0000 88.8784 118.2697 0.0000 101.7484 102.8266 0.0000 89.9008 120.2199 0.0000 102.3626 105.4899 0.0000 90.9103 122.1745 0.0000 102.9640 108.1576 0.0000 91.9112 124.1376 0.0000 103.5569 110.8295 0.0000 92.9035 126.1051 0.0000 104.1325 113.5057 0.0000 93.8829 128.0768 0.0000 104.6952 116.1820 0.0000 94.8494 130.0528 0.0000 105.2494 118.8625 0.0000 95.8031 132.0332 0.0000 105.7863 121.5430 0.0000 96.7438 134.0221 0.0000 106.3147 124.2278 0.0000 97.6717 136.0196 0.0000 106.8302 126.9170 0.0000 98.5781 138.0214 0.0000 107.3371 129.6061 0.0000 99.4630 140.0361 0.0000 107.8397 132.2995 0.0000 100.3265 142.0637 0.0000 108.3337 134.9929 0.0000 101.1641 144.0998 0.0000 108.8320 137.6863 0.0000 101.9760 146.1489 0.0000 109.3346 140.3797 0.0000 102.7664 148.2065 0.0000 109.8458 143.0689 0.0000 103.5354 150.2728 0.0000 110.3699 145.7537 0.0000 104.2828 152.3476 0.0000 110.9111 148.4385 0.0000 105.0174 154.4224 0.0000 111.4653 151.1147 0.0000 105.7348 156.5059 0.0000 112.0280 153.7910 0.0000 106.4436 158.5936 0.0000 112.5865 156.4715 0.0000 107.1481 160.6856 0.0000 113.1277 159.1563 0.0000 107.8440 162.7776 0.0000 113.6432 161.8497 0.0000 108.5485 164.8696 0.0000 114.1200 164.5474 0.0000 109.2659 166.9530 0.0000 114.5496 167.2409 0.0000 110.0047 169.0279 0.0000 114.7429 168.5940 0.0000 110.7608 171.0984 0.0000 114.9362 169.9472 0.0000 111.2548 172.4387 0.0000 115.1768 171.7127 0.0000 111.8132 173.7489 0.0000 115.1682 173.4611 0.0000 112.8313 174.6896 0.0000 113.9310 174.6553 0.0000 113.9310 174.6553 0.0000 −0.0773 0.0816 10.0004 −0.0773 0.0816 10.0004 0.1224 −0.8076 10.0004 −0.2341 1.5207 10.0004 0.3222 −1.6968 10.0004 −0.3909 2.9597 10.0004 0.6057 −2.6505 10.0004 −0.3931 3.6814 10.0004 0.8720 −3.4323 10.0004 −0.3952 4.4031 10.0004 1.5679 −5.1119 10.0004 −0.2019 6.6455 10.0004 1.6410 −5.2665 10.0004 0.2363 8.8578 10.0004 3.0199 −7.7237 10.0004 0.8892 11.0056 10.0004 4.7038 −9.9790 10.0004 1.7355 13.0933 10.0004 6.6455 −12.0194 10.0004 2.7750 15.0823 10.0004 8.7976 −13.8365 10.0004 4.0122 16.9552 10.0004 11.1216 −15.4216 10.0004 5.3997 18.7164 10.0004 13.5788 −16.7963 10.0004 6.8817 20.3961 10.0004 16.1347 −17.9733 10.0004 8.4282 22.0241 10.0004 18.7680 −18.9785 10.0004 10.0090 23.6179 10.0004 21.4528 −19.8247 10.0004 11.6156 25.1901 10.0004 24.1806 −20.5249 10.0004 13.2394 26.7451 10.0004 26.9384 −21.0791 10.0004 14.8632 28.2916 10.0004 29.7264 −21.4743 10.0004 16.4956 29.8338 10.0004 32.5358 −21.6977 10.0004 18.1279 31.3716 10.0004 35.3495 −21.7277 10.0004 19.7646 32.9095 10.0004 38.1589 −21.5430 10.0004 21.3970 34.4474 10.0004 40.9425 −21.1220 10.0004 23.0336 35.9809 10.0004 43.6789 −20.4605 10.0004 24.6660 37.5231 10.0004 46.3422 −19.5498 10.0004 26.3027 39.0610 10.0004 48.9110 −18.3943 10.0004 27.9308 40.6074 10.0004 51.3596 −17.0024 10.0004 29.5588 42.1539 10.0004 53.6750 −15.4001 10.0004 31.1826 43.7046 10.0004 55.8529 −13.6174 10.0004 32.8021 45.2597 10.0004 57.8977 −11.6844 10.0004 34.4087 46.8233 10.0004 59.8136 −9.6224 10.0004 36.0067 48.3955 10.0004 61.6092 −7.4531 10.0004 37.5918 49.9764 10.0004 63.2974 −5.1978 10.0004 39.1641 51.5701 10.0004 64.8868 −2.8738 10.0004 40.7234 53.1724 10.0004 66.3860 −0.4897 10.0004 42.2656 54.7876 10.0004 67.8122 1.9374 10.0004 43.7905 56.4157 10.0004 69.1653 4.4074 10.0004 45.3026 58.0523 10.0004 70.4584 6.9075 10.0004 46.8018 59.7019 10.0004 71.6955 9.4377 10.0004 48.2839 61.3643 10.0004 72.8854 11.9893 10.0004 49.7487 63.0354 10.0004 74.0238 14.5625 10.0004 51.2007 64.7236 10.0004 75.1278 17.1571 10.0004 52.6311 66.4204 10.0004 76.1888 19.7646 10.0004 54.0487 68.1344 10.0004 77.2155 22.3850 10.0004 55.4448 69.8612 10.0004 78.2164 25.0183 10.0004 56.8237 71.6010 10.0004 79.1830 27.6601 10.0004 58.1855 73.3537 10.0004 80.1280 30.3149 10.0004 59.5258 75.1235 10.0004 81.0473 32.9739 10.0004 60.8488 76.9019 10.0004 81.9451 35.6459 10.0004 62.1547 78.7018 10.0004 82.8257 38.3178 10.0004 63.4434 80.5103 10.0004 83.6806 41.0026 10.0004 64.7107 82.3360 10.0004 84.5225 43.6874 10.0004 65.9607 84.1746 10.0004 85.3430 46.3809 10.0004 67.1936 86.0260 10.0004 86.1506 49.0786 10.0004 68.4050 87.8904 10.0004 86.9410 51.7806 10.0004 69.5992 89.7719 10.0004 87.7185 54.4869 10.0004 70.7762 91.6663 10.0004 88.4832 57.1975 10.0004 71.9404 93.5693 10.0004 89.2349 59.9124 10.0004 73.0830 95.4895 10.0004 89.9738 62.6273 10.0004 74.2171 97.4226 10.0004 90.6998 65.3507 10.0004 75.3297 99.3642 10.0004 91.4129 68.0742 10.0004 76.4294 101.3145 10.0004 92.1174 70.7977 10.0004 77.5162 103.2776 10.0004 92.8090 73.5298 10.0004 78.5901 105.2537 10.0004 93.4920 76.2619 10.0004 79.6469 107.2340 10.0004 94.1621 78.9939 10.0004 80.6865 109.2229 10.0004 94.8237 81.7346 10.0004 81.7174 111.2204 10.0004 95.4723 84.4710 10.0004 82.7269 113.2222 10.0004 96.1124 87.2159 10.0004 83.7278 115.2369 10.0004 96.7396 89.9609 10.0004 84.7158 117.2516 10.0004 97.3624 92.7059 10.0004 85.6867 119.2749 10.0004 97.9681 95.4551 10.0004 86.6489 121.2982 10.0004 98.5652 98.2044 10.0004 87.6026 123.3300 10.0004 99.1537 100.9579 10.0004 88.5519 125.3662 10.0004 99.7337 103.7158 10.0004 89.4884 127.4024 10.0004 100.3007 106.4736 10.0004 90.4206 129.4428 10.0004 100.8591 109.2315 10.0004 91.3484 131.4876 10.0004 101.4090 111.9936 10.0004 92.2677 133.5367 10.0004 101.9460 114.7601 10.0004 93.1784 135.5900 10.0004 102.4743 117.5265 10.0004 94.0805 137.6434 10.0004 102.9898 120.2930 10.0004 94.9740 139.7053 10.0004 103.4924 123.0637 10.0004 95.8589 141.7673 10.0004 103.9821 125.8344 10.0004 96.7267 143.8378 10.0004 104.4590 128.6095 10.0004 97.5772 145.9169 10.0004 104.9229 131.3888 10.0004 98.4106 148.0003 10.0004 105.3782 134.1681 10.0004 99.2225 150.0924 10.0004 105.8293 136.9475 10.0004 100.0129 152.1973 10.0004 106.2760 139.7268 10.0004 100.7818 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40.0017 86.9926 134.0822 40.0017 100.4940 122.0027 40.0017 87.8775 136.2644 40.0017 101.0052 124.9839 40.0017 88.7581 138.4510 40.0017 101.5078 127.9651 40.0017 89.6344 140.6332 40.0017 102.0018 130.9463 40.0017 90.5108 142.8197 40.0017 102.4872 133.9319 40.0017 91.3828 145.0105 40.0017 102.9683 136.9174 40.0017 92.2505 147.1970 40.0017 103.4366 139.9072 40.0017 93.1183 149.3922 40.0017 103.9005 142.8927 40.0017 93.9774 151.5830 40.0017 104.3602 145.8826 40.0017 94.8323 153.7781 40.0017 104.8155 148.8767 40.0017 95.6785 155.9775 40.0017 105.2708 151.8665 40.0017 96.5162 158.1769 40.0017 105.7262 154.8563 40.0017 97.3410 160.3806 40.0017 106.1944 157.8461 40.0017 98.1571 162.5929 40.0017 106.6798 160.8317 40.0017 98.9561 164.8095 40.0017 107.1867 163.8129 40.0017 99.7380 167.0304 40.0017 107.7151 166.7898 40.0017 100.5069 169.2556 40.0017 108.2736 169.7582 40.0017 101.2501 171.4893 40.0017 108.8535 172.7265 40.0017 101.9803 173.7317 40.0017 109.4506 175.6948 40.0017 102.6891 175.9783 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−22.6986 50.0021 7.6593 20.3230 50.0021 23.6393 −23.9916 50.0021 9.4635 21.8824 50.0021 26.5261 −25.1085 50.0021 11.3192 23.3859 50.0021 29.4772 −26.0063 50.0021 13.2050 24.8593 50.0021 32.4928 −26.6420 50.0021 15.0909 26.3242 50.0021 35.5857 −26.9556 50.0021 16.9724 27.7976 50.0021 38.6700 −26.8912 50.0021 18.8367 29.2839 50.0021 41.7243 −26.4144 50.0021 20.6882 30.7917 50.0021 44.6969 −25.5123 50.0021 22.5181 32.3253 50.0021 47.5020 −24.2278 50.0021 24.3309 33.8803 50.0021 50.1482 −22.6084 50.0021 26.1266 35.4568 50.0021 52.6054 −20.7182 50.0021 27.8964 37.0549 50.0021 54.8735 −18.6176 50.0021 29.6490 38.6743 50.0021 56.9741 −16.3409 50.0021 31.3759 40.3239 50.0021 58.9244 −13.9310 50.0021 33.0856 41.9992 50.0021 60.7328 −11.4395 50.0021 34.7695 43.7003 50.0021 62.4168 −8.8835 50.0021 36.4277 45.4229 50.0021 64.0062 −6.2632 50.0021 38.0515 47.1713 50.0021 65.5054 −3.5955 50.0021 39.6495 48.9411 50.0021 66.9273 −0.8849 50.0021 41.2131 50.7367 50.0021 68.2847 1.8600 50.0021 42.7424 52.5495 50.0021 69.5863 4.6437 50.0021 44.2416 54.3838 50.0021 70.8321 7.4574 50.0021 45.7107 56.2395 50.0021 72.0263 10.2925 50.0021 47.1541 58.1125 50.0021 73.1732 13.1492 50.0021 48.5674 60.0069 50.0021 74.2772 16.0187 50.0021 49.9549 61.9228 50.0021 75.3426 18.9012 50.0021 51.3166 63.8515 50.0021 76.3693 21.7922 50.0021 52.6569 65.7975 50.0021 77.3659 24.6918 50.0021 53.9757 67.7563 50.0021 78.3367 27.6043 50.0021 55.2730 69.7324 50.0021 79.2775 30.5211 50.0021 56.5445 71.7256 50.0021 80.1967 33.4465 50.0021 57.7989 73.7317 50.0021 81.0945 36.3804 50.0021 59.0317 75.7507 50.0021 81.9666 39.3230 50.0021 60.2474 77.7826 50.0021 82.8214 42.2699 50.0021 61.4416 79.8273 50.0021 83.6548 45.2210 50.0021 62.6144 81.8850 50.0021 84.4753 48.1765 50.0021 63.7742 83.9598 50.0021 85.2743 51.1405 50.0021 64.9169 86.0432 50.0021 86.0604 54.1089 50.0021 66.0381 88.1395 50.0021 86.8293 57.0815 50.0021 67.1464 90.2444 50.0021 87.5811 60.0627 50.0021 68.2375 92.3579 50.0021 88.3199 63.0439 50.0021 69.3114 94.4843 50.0021 89.0459 66.0295 50.0021 70.3724 96.6150 50.0021 89.7590 69.0150 50.0021 71.4163 98.7499 50.0021 90.4635 72.0091 50.0021 72.4473 100.8978 50.0021 91.1508 74.9989 50.0021 73.4611 103.0500 50.0021 91.8295 77.9973 50.0021 74.4620 105.2064 50.0021 92.4954 80.9957 50.0021 75.4500 107.3672 50.0021 93.1526 83.9942 50.0021 76.4294 109.5322 50.0021 93.8013 86.9969 50.0021 77.3959 111.7058 50.0021 94.4370 90.0039 50.0021 78.3539 113.8795 50.0021 95.0642 93.0066 50.0021 79.2989 116.0617 50.0021 95.6828 96.0179 50.0021 80.2354 118.2439 50.0021 96.2928 99.0292 50.0021 81.1676 120.4347 50.0021 96.8899 102.0405 50.0021 82.0869 122.6255 50.0021 97.4827 105.0518 50.0021 83.0018 124.8207 50.0021 98.0626 108.0674 50.0021 83.9082 127.0158 50.0021 98.6383 111.0872 50.0021 84.8103 129.2195 50.0021 99.2053 114.1071 50.0021 85.7081 131.4232 50.0021 99.7594 117.1270 50.0021 86.5974 133.6269 50.0021 100.3093 120.1512 50.0021 87.4823 135.8349 50.0021 100.8506 123.1754 50.0021 88.3629 138.0429 50.0021 101.3832 126.1996 50.0021 89.2392 140.2552 50.0021 101.9073 129.2281 50.0021 90.1156 142.4675 50.0021 102.4228 132.2565 50.0021 90.9876 144.6798 50.0021 102.9297 135.2893 50.0021 91.8639 146.8920 50.0021 103.4280 138.3178 50.0021 92.7359 149.1043 50.0021 103.9220 141.3506 50.0021 93.6037 151.3166 50.0021 104.4031 144.3833 50.0021 94.4714 153.5332 50.0021 104.8842 147.4204 50.0021 95.3391 155.7498 50.0021 105.3568 150.4532 50.0021 96.1983 157.9664 50.0021 105.8293 153.4903 50.0021 97.0488 160.1873 50.0021 106.3061 156.5273 50.0021 97.8865 162.4168 50.0021 106.7872 159.5601 50.0021 98.7156 164.6462 50.0021 107.2855 162.5929 50.0021 99.5275 166.8800 50.0021 107.8139 165.6214 50.0021 100.3265 169.1224 50.0021 108.3681 168.6413 50.0021 101.1083 171.3690 50.0021 108.9609 171.6569 50.0021 101.8729 173.6200 50.0021 109.5837 174.6639 50.0021 102.6247 175.8795 50.0021 110.2195 177.6752 50.0021 103.3635 178.1391 50.0021 110.8424 180.6865 50.0021 104.0938 180.4029 50.0021 111.4309 183.7063 50.0021 104.8284 182.6668 50.0021 111.9722 186.7348 50.0021 105.5715 184.9263 50.0021 112.4876 189.7590 50.0021 106.3448 187.1773 50.0021 113.0160 192.7875 50.0021 107.1610 189.4111 50.0021 113.1900 193.7734 50.0021 108.0201 191.6276 50.0021 113.3640 194.7592 50.0021 108.8492 193.8614 50.0021 113.1664 196.6923 50.0021 109.6868 196.0823 50.0021 111.4524 197.4913 50.0021 111.4524 197.4913 50.0021 −0.6315 1.8557 60.0026 −0.6315 1.8557 60.0026 −0.3265 −1.3016 60.0026 −0.5606 3.3979 60.0026 0.4425 −4.3258 60.0026 −0.4897 4.9401 60.0026 1.6367 −7.2383 60.0026 −0.2406 6.4651 60.0026 3.2261 −9.9575 60.0026 0.0494 7.6206 60.0026 5.1291 −12.4533 60.0026 0.3394 8.7762 60.0026 7.3500 −14.6914 60.0026 1.1770 11.0142 60.0026 9.7556 −16.6975 60.0026 2.2467 13.1492 60.0026 12.2686 −18.5489 60.0026 3.5311 15.1639 60.0026 14.8589 −20.3102 60.0026 5.0088 17.0368 60.0026 17.5093 −21.9812 60.0026 6.6584 18.7680 60.0026 20.2328 −23.5362 60.0026 8.4368 20.3617 60.0026 23.0207 −24.9452 60.0026 10.2968 21.8566 60.0026 25.8817 −26.1738 60.0026 12.1955 23.3043 60.0026 28.8500 −27.1833 60.0026 14.1114 24.7347 60.0026 31.9043 −27.9179 60.0026 16.0230 26.1652 60.0026 35.0187 −28.3088 60.0026 17.9174 27.6172 60.0026 38.1632 −28.2959 60.0026 19.7990 29.0863 60.0026 41.2518 −27.8362 60.0026 21.6590 30.5855 60.0026 44.2287 −26.9341 60.0026 23.4976 32.1105 60.0026 47.0854 −25.6240 60.0026 25.3190 33.6569 60.0026 49.7487 −23.9830 60.0026 27.1146 35.2292 60.0026 52.2230 −22.0585 60.0026 28.8887 36.8272 60.0026 54.5084 −19.9064 60.0026 30.6414 38.4510 60.0026 56.6004 −17.6124 60.0026 32.3639 40.1048 60.0026 58.5334 −15.2068 60.0026 34.0607 41.7844 60.0026 60.3376 −12.7110 60.0026 35.7318 43.4941 60.0026 62.0345 −10.1379 60.0026 37.3727 45.2296 60.0026 63.6325 −7.4960 60.0026 38.9836 46.9951 60.0026 65.1531 −4.7983 60.0026 40.5602 48.7822 60.0026 66.5965 −2.0491 60.0026 42.1109 50.5993 60.0026 67.9797 0.7389 60.0026 43.6316 52.4421 60.0026 69.2985 3.5483 60.0026 45.1222 54.3065 60.0026 70.5572 6.3877 60.0026 46.5871 56.1966 60.0026 71.7685 9.2444 60.0026 48.0218 58.1039 60.0026 72.9284 12.1225 60.0026 49.4308 60.0326 60.0026 74.0496 15.0221 60.0026 50.8097 61.9829 60.0026 75.1321 17.9346 60.0026 52.1672 63.9460 60.0026 76.1802 20.8557 60.0026 53.4989 65.9307 60.0026 77.1983 23.7940 60.0026 54.8091 67.9282 60.0026 78.1906 26.7365 60.0026 56.0935 69.9429 60.0026 79.1529 29.6920 60.0026 57.3521 71.9704 60.0026 80.0936 32.6517 60.0026 58.5936 74.0109 60.0026 81.0129 35.6201 60.0026 59.8136 76.0643 60.0026 81.9064 38.5927 60.0026 61.0121 78.1305 60.0026 82.7828 41.5740 60.0026 62.1891 80.2096 60.0026 83.6376 44.5595 60.0026 63.3489 82.2973 60.0026 84.4753 47.5536 60.0026 64.4916 84.3937 60.0026 85.2958 50.5520 60.0026 65.6128 86.5029 60.0026 86.0991 53.5504 60.0026 66.7168 88.6206 60.0026 86.8852 56.5574 60.0026 67.8036 90.7470 60.0026 87.6584 59.5644 60.0026 68.8775 92.8820 60.0026 88.4145 62.5757 60.0026 69.9343 95.0213 60.0026 89.1576 65.5913 60.0026 70.9738 97.1734 60.0026 89.8879 68.6112 60.0026 72.0005 99.3299 60.0026 90.6096 71.6311 60.0026 73.0143 101.4906 60.0026 91.3141 74.6553 60.0026 74.0152 103.6600 60.0026 92.0143 77.6795 60.0026 75.0032 105.8336 60.0026 92.6973 80.7079 60.0026 75.9826 108.0115 60.0026 93.3760 83.7407 60.0026 76.9492 110.1937 60.0026 94.0418 86.7735 60.0026 77.9071 112.3846 60.0026 94.6991 89.8106 60.0026 78.8565 114.5754 60.0026 95.3477 92.8476 60.0026 79.7972 116.7705 60.0026 95.9921 95.8847 60.0026 80.7251 118.9699 60.0026 96.6236 98.9261 60.0026 81.6487 121.1736 60.0026 97.2464 101.9674 60.0026 82.5637 123.3773 60.0026 97.8607 105.0131 60.0026 83.4744 125.5853 60.0026 98.4621 108.0631 60.0026 84.3765 127.7976 60.0026 99.0592 111.1087 60.0026 85.2786 130.0099 60.0026 99.6435 114.1630 60.0026 86.1721 132.2222 60.0026 100.2191 117.2129 60.0026 87.0699 134.4388 60.0026 100.7904 120.2672 60.0026 87.9634 136.6511 60.0026 101.3489 123.3214 60.0026 88.8526 138.8676 60.0026 101.9073 126.3800 60.0026 89.7418 141.0842 60.0026 102.4529 129.4343 60.0026 90.6310 143.3008 60.0026 102.9984 132.4928 60.0026 91.5203 145.5174 60.0026 103.5311 135.5514 60.0026 92.4095 147.7340 60.0026 104.0595 138.6142 60.0026 93.2944 149.9549 60.0026 104.5792 141.6728 60.0026 94.1750 152.1715 60.0026 105.0904 144.7399 60.0026 95.0556 154.3924 60.0026 105.5930 147.8027 60.0026 95.9363 156.6133 60.0026 106.0870 150.8699 60.0026 96.8083 158.8341 60.0026 106.5810 153.9370 60.0026 97.6803 161.0593 60.0026 107.0750 157.0042 60.0026 98.5480 163.2845 60.0026 107.5819 160.0713 60.0026 99.4029 165.5140 60.0026 108.1103 163.1299 60.0026 100.2492 167.7478 60.0026 108.6688 166.1841 60.0026 101.0739 169.9901 60.0026 109.2573 169.2341 60.0026 101.8772 172.2368 60.0026 109.8801 172.2754 60.0026 102.6633 174.4920 60.0026 110.5245 175.3168 60.0026 103.4366 176.7559 60.0026 111.1775 178.3539 60.0026 104.2012 179.0154 60.0026 111.8218 181.3910 60.0026 104.9701 181.2793 60.0026 112.4361 184.4366 60.0026 105.7563 183.5345 60.0026 113.0203 187.4866 60.0026 106.5596 185.7812 60.0026 113.5788 190.5408 60.0026 107.3843 188.0192 60.0026 114.1673 193.5951 60.0026 108.2263 190.2573 60.0026 114.3327 194.5852 60.0026 109.0769 192.4868 60.0026 114.4980 195.5754 60.0026 109.9360 194.7163 60.0026 114.3133 197.5386 60.0026 110.8553 196.9243 60.0026 112.5907 198.3848 60.0026 112.5907 198.3848 60.0026 −0.6916 2.0362 70.0030 −0.6916 2.0362 70.0030 −0.5241 −1.0610 70.0030 −0.6100 3.5740 70.0030 0.1117 −4.0938 70.0030 −0.4253 5.1033 70.0030 1.1341 −7.0149 70.0030 −0.1203 6.6240 70.0030 2.5645 −9.7642 70.0030 0.2191 7.7710 70.0030 4.3172 −12.3158 70.0030 0.5584 8.9179 70.0030 6.3791 −14.6269 70.0030 1.4734 11.1044 70.0030 8.6645 −16.7189 70.0030 2.6247 13.1964 70.0030 11.0787 −18.6649 70.0030 3.9864 15.1682 70.0030 13.5702 −20.5120 70.0030 5.5329 16.9853 70.0030 16.1132 −22.2776 70.0030 7.2426 18.6520 70.0030 18.7250 −23.9486 70.0030 9.0811 20.1899 70.0030 21.4142 −25.4908 70.0030 11.0013 21.6418 70.0030 24.1935 −26.8654 70.0030 12.9602 23.0422 70.0030 27.0630 −28.0424 70.0030 14.9233 24.4297 70.0030 30.0185 −28.9703 70.0030 16.8865 25.8259 70.0030 33.0512 −29.5803 70.0030 18.8324 27.2391 70.0030 36.1442 −29.8166 70.0030 20.7569 28.6825 70.0030 39.2285 −29.6233 70.0030 22.6599 30.1516 70.0030 42.2527 −28.9789 70.0030 24.5371 31.6508 70.0030 45.1609 −27.9136 70.0030 26.3929 33.1715 70.0030 47.9144 −26.4831 70.0030 28.2272 34.7266 70.0030 50.4704 −24.7433 70.0030 30.0314 36.3203 70.0030 52.8373 −22.7501 70.0030 31.8098 37.9441 70.0030 55.0324 −20.5593 70.0030 33.5581 39.6065 70.0030 57.0772 −18.2267 70.0030 35.2764 41.3033 70.0030 58.9802 −15.7782 70.0030 36.9561 43.0302 70.0030 60.7629 −13.2394 70.0030 38.5970 44.7914 70.0030 62.4425 −10.6319 70.0030 40.1950 46.5828 70.0030 64.0234 −7.9686 70.0030 41.7544 48.3955 70.0030 65.5269 −5.2623 70.0030 43.2794 50.2341 70.0030 66.9616 −2.5173 70.0030 44.7700 52.0985 70.0030 68.3277 0.2663 70.0030 46.2305 53.9843 70.0030 69.6336 3.0757 70.0030 47.6610 55.8916 70.0030 70.8879 5.9109 70.0030 49.0614 57.8204 70.0030 72.0907 8.7676 70.0030 50.4360 59.7663 70.0030 73.2506 11.6457 70.0030 51.7806 61.7295 70.0030 74.3675 14.5410 70.0030 53.1037 63.7141 70.0030 75.4543 17.4449 70.0030 54.3967 65.7159 70.0030 76.5067 20.3617 70.0030 55.6682 67.7349 70.0030 77.5291 23.2871 70.0030 56.9183 69.7667 70.0030 78.5257 26.2211 70.0030 58.1425 71.8158 70.0030 79.4965 29.1636 70.0030 59.3496 73.8820 70.0030 80.4416 32.1105 70.0030 60.5352 75.9569 70.0030 81.3652 35.0702 70.0030 61.7037 78.0489 70.0030 82.2673 38.0343 70.0030 62.8549 80.1538 70.0030 83.1479 41.0026 70.0030 63.9847 82.2673 70.0030 84.0113 43.9796 70.0030 65.1016 84.3894 70.0030 84.8576 46.9608 70.0030 66.2013 86.5243 70.0030 85.6824 49.9463 70.0030 67.2838 88.6636 70.0030 86.4943 52.9361 70.0030 68.3492 90.8115 70.0030 87.2890 55.9345 70.0030 69.4059 92.9679 70.0030 88.0708 58.9372 70.0030 70.4412 95.1244 70.0030 88.8397 61.9442 70.0030 71.4678 97.2894 70.0030 89.5958 64.9555 70.0030 72.4859 99.4587 70.0030 90.3346 67.9668 70.0030 73.4868 101.6367 70.0030 91.0649 70.9695 70.0030 74.4791 103.8146 70.0030 91.7823 73.9851 70.0030 75.4629 106.0011 70.0030 92.5126 77.0909 70.0030 76.4337 108.1876 70.0030 93.2428 80.2397 70.0030 77.3959 110.3827 70.0030 93.9559 83.3842 70.0030 78.3539 112.5779 70.0030 94.6604 86.5200 70.0030 79.2989 114.7816 70.0030 95.3520 89.6516 70.0030 80.2397 116.9853 70.0030 96.0308 92.7832 70.0030 81.1719 119.1933 70.0030 96.7009 95.9148 70.0030 82.0997 121.4013 70.0030 97.3624 99.0506 70.0030 83.0190 123.6136 70.0030 98.0154 102.1908 70.0030 83.9383 125.8301 70.0030 98.6554 105.3353 70.0030 84.8490 128.0467 70.0030 99.2912 108.4840 70.0030 85.7597 130.2633 70.0030 99.9141 111.6328 70.0030 86.6704 132.4799 70.0030 100.5327 114.7902 70.0030 87.5768 134.6965 70.0030 101.1427 117.9432 70.0030 88.4832 136.9174 70.0030 101.7441 121.1006 70.0030 89.3896 139.1340 70.0030 102.3369 124.2622 70.0030 90.2960 141.3549 70.0030 102.9211 127.4196 70.0030 91.2067 143.5715 70.0030 103.4967 130.5812 70.0030 92.1174 145.7880 70.0030 104.0680 133.7429 70.0030 93.0281 148.0046 70.0030 104.6308 136.9045 70.0030 93.9430 150.2212 70.0030 105.1849 140.0704 70.0030 94.8580 152.4378 70.0030 105.7348 143.2364 70.0030 95.7687 154.6544 70.0030 106.2760 146.3980 70.0030 96.6794 156.8710 70.0030 106.8130 149.5683 70.0030 97.5901 159.0876 70.0030 107.3414 152.7342 70.0030 98.4922 161.3085 70.0030 107.8740 155.9045 70.0030 99.3857 163.5337 70.0030 108.4067 159.0704 70.0030 100.2663 165.7631 70.0030 108.9609 162.2321 70.0030 101.1384 167.9926 70.0030 109.5408 165.3937 70.0030 101.9932 170.2350 70.0030 110.1551 168.5425 70.0030 102.8309 172.4773 70.0030 110.8037 171.6869 70.0030 103.6600 174.7283 70.0030 111.4782 174.8271 70.0030 104.4718 176.9835 70.0030 112.1741 177.9630 70.0030 105.2751 179.2431 70.0030 112.8614 181.1031 70.0030 106.0741 181.5026 70.0030 113.5358 184.2433 70.0030 106.8774 183.7579 70.0030 114.1845 187.3878 70.0030 107.6979 186.0088 70.0030 114.8030 190.5365 70.0030 108.5442 188.2555 70.0030 115.3830 193.6982 70.0030 109.4162 190.4850 70.0030 115.5355 194.7227 70.0030 110.3011 192.7145 70.0030 115.6880 195.7472 70.0030 111.1818 194.9396 70.0030 115.6622 197.7791 70.0030 112.1010 197.1562 70.0030 113.8580 198.5996 70.0030 113.8580 198.5996 70.0030 −0.7174 1.9245 79.9991 −0.7174 1.9245 79.9991 −0.6401 −1.2286 79.9991 −0.5842 3.4709 79.9991 −0.0988 −4.3301 79.9991 −0.3394 5.0045 79.9991 0.8591 −7.3285 79.9991 0.0215 6.5252 79.9991 2.2252 −10.1680 79.9991 0.3995 7.6657 79.9991 3.9435 −12.8098 79.9991 0.7775 8.8062 79.9991 5.9796 −15.2111 79.9991 1.7741 10.9799 79.9991 8.2435 −17.4062 79.9991 3.0113 13.0504 79.9991 10.6448 −19.4510 79.9991 4.4504 14.9792 79.9991 13.1277 −21.3927 79.9991 6.0698 16.7490 79.9991 15.6708 −23.2570 79.9991 7.8569 18.3642 79.9991 18.2869 −25.0140 79.9991 9.7599 19.8505 79.9991 20.9975 −26.6377 79.9991 11.7445 21.2423 79.9991 23.7983 −28.0811 79.9991 13.7592 22.5912 79.9991 26.7022 −29.3183 79.9991 15.7782 23.9228 79.9991 29.7049 −30.2848 79.9991 17.7972 25.2631 79.9991 32.7892 −30.9206 79.9991 19.8033 26.6206 79.9991 35.9337 −31.1568 79.9991 21.7879 28.0081 79.9991 39.0781 −30.9549 79.9991 23.7510 29.4214 79.9991 42.1539 −30.2891 79.9991 25.6841 30.8733 79.9991 45.1050 −29.1894 79.9991 27.5914 32.3596 79.9991 47.8972 −27.7160 79.9991 29.4686 33.8889 79.9991 50.4919 −25.9332 79.9991 31.3158 35.4654 79.9991 52.8975 −23.9014 79.9991 33.1243 37.0849 79.9991 55.1269 −21.6719 79.9991 34.8984 38.7474 79.9991 57.2018 −19.2964 79.9991 36.6253 40.4528 79.9991 59.1391 −16.8048 79.9991 38.3049 42.2011 79.9991 60.9562 −14.2231 79.9991 39.9330 43.9796 79.9991 62.6702 −11.5770 79.9991 41.5181 45.7966 79.9991 64.2854 −8.8750 79.9991 43.0517 47.6395 79.9991 65.8233 −6.1214 79.9991 44.5509 49.5124 79.9991 67.2881 −3.3335 79.9991 46.0157 51.4154 79.9991 68.6842 −0.5069 79.9991 47.4462 53.3399 79.9991 70.0202 2.3455 79.9991 48.8423 55.2902 79.9991 71.3046 5.2279 79.9991 50.2126 57.2576 79.9991 72.5375 8.1318 79.9991 51.5529 59.2465 79.9991 73.7231 11.0529 79.9991 52.8631 61.2569 79.9991 74.8658 13.9912 79.9991 54.1475 63.2845 79.9991 75.9783 16.9466 79.9991 55.4105 65.3293 79.9991 77.0566 19.9064 79.9991 56.6476 67.3955 79.9991 78.1004 22.8790 79.9991 57.8676 69.4746 79.9991 79.1185 25.8645 79.9991 59.0618 71.5709 79.9991 80.1108 28.8543 79.9991 60.2388 73.6801 79.9991 81.0774 31.8527 79.9991 61.3944 75.7979 79.9991 82.0224 34.8597 79.9991 62.5328 77.9286 79.9991 82.9460 37.8710 79.9991 63.6496 80.0636 79.9991 83.8524 40.8909 79.9991 64.7536 82.2114 79.9991 84.7330 43.9151 79.9991 65.8405 84.3636 79.9991 85.6008 46.9479 79.9991 66.9144 86.5243 79.9991 86.4470 49.9850 79.9991 67.9754 88.6894 79.9991 87.2761 53.0263 79.9991 69.0236 90.8587 79.9991 88.0923 56.0720 79.9991 70.0589 93.0366 79.9991 88.8913 59.1220 79.9991 71.0855 95.2146 79.9991 89.6774 62.1762 79.9991 72.0993 97.4011 79.9991 90.4506 65.2348 79.9991 73.1088 99.5919 79.9991 91.2110 68.2976 79.9991 74.1054 101.7870 79.9991 91.9584 71.3562 79.9991 75.0934 103.9821 79.9991 −0.7432 −1.6710 89.9996 −0.5584 3.1101 89.9996 −0.2663 −4.8628 89.9996 −0.2620 4.6609 89.9996 0.6444 −7.9256 89.9996 0.1418 6.1901 89.9996 1.9846 −10.8682 89.9996 0.5584 7.3285 89.9996 3.6900 −13.5959 89.9996 0.9751 8.4669 89.9996 5.7262 −16.0832 89.9996 2.0576 10.6405 89.9996 8.0072 −18.3771 89.9996 3.3807 12.6981 89.9996 10.4257 −20.5206 89.9996 4.8971 14.5926 89.9996 12.9215 −22.5568 89.9996 6.6025 16.3237 89.9996 15.4947 −24.5114 89.9996 8.4712 17.8960 89.9996 18.1537 −26.3499 89.9996 10.4472 19.3307 89.9996 20.9030 −28.0339 89.9996 12.4791 20.6667 89.9996 23.7467 −29.5159 89.9996 14.5453 21.9511 89.9996 26.7108 −30.7702 89.9996 16.6201 23.2269 89.9996 29.7994 −31.7411 89.9996 18.6907 24.5114 89.9996 32.9739 −32.3425 89.9996 20.7483 25.8216 89.9996 36.2043 −32.5057 89.9996 22.7759 27.1575 89.9996 39.4218 −32.2050 89.9996 24.7734 28.5322 89.9996 42.5491 −31.4232 89.9996 26.7322 29.9454 89.9996 45.5432 −30.1903 89.9996 28.6567 31.4017 89.9996 48.3354 −28.5966 89.9996 30.5340 32.9052 89.9996 50.9515 −26.6893 89.9996 32.3725 34.4559 89.9996 53.3700 −24.5414 89.9996 34.1638 36.0540 89.9996 55.6038 −22.2132 89.9996 35.9122 37.7035 89.9996 57.6915 −19.7431 89.9996 37.6133 39.4003 89.9996 59.6374 −17.1657 89.9996 39.2672 41.1487 89.9996 61.4545 −14.5238 89.9996 40.8780 42.9443 89.9996 63.1556 −11.8304 89.9996 42.4460 44.7914 89.9996 64.7708 −9.0897 89.9996 43.9753 46.6773 89.9996 66.3044 −6.3104 89.9996 45.4659 48.6017 89.9996 67.7649 −3.4924 89.9996 46.9178 50.5520 89.9996 69.1610 −0.6444 89.9996 48.3311 52.5280 89.9996 70.4970 2.2295 89.9996 49.7057 54.5212 89.9996 71.7857 5.1377 89.9996 51.0503 56.5316 89.9996 73.0229 8.0631 89.9996 52.3605 58.5635 89.9996 74.2128 11.0142 89.9996 53.6406 60.6083 89.9996 75.3727 13.9826 89.9996 54.8950 62.6702 89.9996 76.4938 16.9681 89.9996 56.1235 64.7450 89.9996 77.5849 19.9665 89.9996 57.3306 66.8328 89.9996 78.6460 22.9778 89.9996 58.5163 68.9334 89.9996 79.6770 26.0020 89.9996 59.6847 71.0426 89.9996 80.6865 29.0305 89.9996 60.8317 73.1647 89.9996 81.6702 32.0718 89.9996 61.9614 75.2996 89.9996 82.6324 35.1132 89.9996 63.0740 77.4389 89.9996 83.5689 38.1632 89.9996 64.1737 79.5868 89.9996 84.4925 41.2217 89.9996 65.2562 81.7432 89.9996 85.3903 44.2803 89.9996 66.3302 83.9082 89.9996 86.2752 47.3474 89.9996 67.3912 86.0776 89.9996 87.1386 50.4231 89.9996 68.4394 88.2512 89.9996 87.9892 53.4989 89.9996 69.4832 90.4334 89.9996 88.8182 56.5832 89.9996 70.5142 92.6200 89.9996 89.6387 59.6675 89.9996 71.5366 94.8151 89.9996 90.4420 62.7604 89.9996 72.5504 97.0102 89.9996 91.2281 65.8533 89.9996 73.5556 99.2096 89.9996 92.0057 68.9506 89.9996 74.5565 101.4133 89.9996 92.7703 72.0521 89.9996 75.5488 103.6213 89.9996 93.5221 75.1536 89.9996 76.5325 105.8293 89.9996 94.2652 78.2594 89.9996 77.5119 108.0416 89.9996 94.9955 81.3652 89.9996 78.4870 110.2539 89.9996 95.7172 84.4753 89.9996 79.4579 112.4705 89.9996 96.4303 87.5897 89.9996 80.4244 114.6914 89.9996 97.1305 90.7041 89.9996 81.3867 116.9122 89.9996 97.8221 93.8185 89.9996 82.3446 119.1331 89.9996 98.5051 96.9372 89.9996 83.2983 121.3540 89.9996 99.1838 100.0558 89.9996 84.2519 123.5792 89.9996 99.8496 103.1788 89.9996 85.2013 125.8044 89.9996 100.5112 106.2975 89.9996 86.1506 128.0253 89.9996 101.1641 109.4248 89.9996 87.1000 130.2504 89.9996 101.8128 112.5478 89.9996 88.0493 132.4799 89.9996 102.4529 115.6751 89.9996 88.9987 134.7051 89.9996 103.0800 118.8066 89.9996 89.9480 136.9303 89.9996 103.7029 121.9382 89.9996 90.9017 139.1512 89.9996 104.3172 125.0698 89.9996 91.8553 141.3763 89.9996 104.9186 128.2057 89.9996 92.8090 143.5972 89.9996 105.5157 131.3416 89.9996 93.7669 145.8224 89.9996 106.0999 134.4817 89.9996 94.7249 148.0433 89.9996 106.6755 137.6219 89.9996 95.6871 150.2642 89.9996 107.2426 140.7664 89.9996 96.6493 152.4851 89.9996 107.8053 143.9108 89.9996 97.6073 154.7017 89.9996 108.3681 147.0553 89.9996 98.5652 156.9268 89.9996 108.9308 150.1955 89.9996 99.5189 159.1477 89.9996 109.4935 153.3399 89.9996 100.4682 161.3729 89.9996 110.0649 156.4844 89.9996 101.4090 163.6024 89.9996 110.6448 159.6246 89.9996 102.3412 165.8362 89.9996 111.2376 162.7604 89.9996 103.2604 168.0742 89.9996 111.8519 165.8963 89.9996 104.1625 170.3209 89.9996 112.4876 169.0236 89.9996 105.0432 172.5718 89.9996 113.1492 172.1466 89.9996 105.9066 174.8314 89.9996 113.8408 175.2653 89.9996 106.7529 177.0995 89.9996 114.5668 178.3797 89.9996 107.5819 179.3720 89.9996 115.3142 181.4855 89.9996 108.4067 181.6487 89.9996 116.0617 184.5913 89.9996 109.2401 183.9168 89.9996 116.7447 187.7142 89.9996 110.0992 186.1807 89.9996 117.3375 190.8544 89.9996 110.9884 188.4316 89.9996 117.9518 193.9903 89.9996 111.9077 190.6697 89.9996 118.1580 194.9998 89.9996 112.8442 192.8992 89.9996 118.3642 196.0093 89.9996 113.7549 195.1415 89.9996 118.2310 198.0197 89.9996 114.6570 197.3796 89.9996 116.4569 198.8573 89.9996 116.4569 198.8573 89.9996 −0.7475 1.0310 100.0000 −0.7475 1.0310 100.0000 −0.8634 −1.0353 100.0000 −0.5284 2.5560 100.0000 −0.7775 −3.1058 100.0000 −0.1976 4.0766 100.0000 −0.4983 −5.1763 100.0000 0.2449 5.5672 100.0000 −0.0988 −6.7400 100.0000 0.6830 6.6820 100.0000 0.3007 −8.3036 100.0000 1.1212 7.7967 100.0000 1.5121 −11.2591 100.0000 2.2295 9.9145 100.0000 3.1101 −14.0642 100.0000 3.5697 11.9163 100.0000 5.0475 −16.6459 100.0000 5.1033 13.7549 100.0000 7.2383 −19.0043 100.0000 6.8130 15.4216 100.0000 9.5837 −21.2208 100.0000 8.6816 16.9380 100.0000 12.0151 −23.3429 100.0000 10.6620 18.3212 100.0000 14.5195 −25.3619 100.0000 12.7067 19.6014 100.0000 17.1013 −27.2692 100.0000 14.7902 20.8299 100.0000 19.7947 −29.0348 100.0000 16.8779 22.0456 100.0000 22.6127 −30.6156 100.0000 18.9570 23.2785 100.0000 25.5595 −31.9687 100.0000 21.0189 24.5414 100.0000 28.6009 −33.0255 100.0000 23.0465 25.8516 100.0000 31.7582 −33.7300 100.0000 25.0397 27.2048 100.0000 34.9886 −34.0135 100.0000 26.9986 28.6095 100.0000 38.2018 −33.8159 100.0000 28.9188 30.0657 100.0000 41.3806 −33.1243 100.0000 30.8046 31.5821 100.0000 44.3962 −31.9816 100.0000 32.6475 33.1586 100.0000 47.2529 −30.4480 100.0000 34.4517 34.7867 100.0000 49.9162 −28.5966 100.0000 36.2000 36.4706 100.0000 52.3691 −26.5003 100.0000 37.9011 38.1975 100.0000 54.6544 −24.2021 100.0000 39.5464 39.9674 100.0000 56.7722 −21.7621 100.0000 41.1401 41.7716 100.0000 58.7396 −19.2319 100.0000 42.6822 43.6187 100.0000 60.5782 −16.6287 100.0000 44.1857 45.4959 100.0000 62.3094 −13.9611 100.0000 45.6463 47.4075 100.0000 63.9503 −11.2376 100.0000 47.0682 49.3449 100.0000 65.5097 −8.4669 100.0000 48.4514 51.3123 100.0000 67.0003 −5.6575 100.0000 49.8088 53.3056 100.0000 68.4265 −2.8137 100.0000 51.1319 55.3202 100.0000 69.7968 0.0687 100.0000 52.4292 57.3607 100.0000 71.1156 2.9855 100.0000 53.7008 59.4184 100.0000 72.3871 5.9238 100.0000 54.9465 61.4889 100.0000 73.6114 8.8835 100.0000 56.1708 63.5766 100.0000 74.7970 11.8605 100.0000 57.3736 65.6729 100.0000 75.9483 14.8460 100.0000 58.5549 67.7778 100.0000 77.0652 17.8487 100.0000 59.7191 69.8956 100.0000 78.1563 20.8557 100.0000 60.8660 72.0177 100.0000 79.2173 23.8756 100.0000 62.0001 74.1527 100.0000 80.2526 26.9041 100.0000 63.1170 76.2876 100.0000 81.2621 29.9411 100.0000 64.2167 78.4355 100.0000 82.2544 32.9868 100.0000 65.3078 80.5834 100.0000 83.2209 36.0411 100.0000 66.3860 82.7441 100.0000 84.1703 39.0996 100.0000 67.4556 84.9048 100.0000 85.0982 42.1668 100.0000 68.5124 87.0742 100.0000 86.0088 45.2339 100.0000 69.5563 89.2435 100.0000 86.8981 48.3096 100.0000 70.5958 91.4215 100.0000 87.7744 51.3897 100.0000 71.6225 93.6037 100.0000 88.6378 54.4740 100.0000 72.6449 95.7902 100.0000 89.4798 57.5626 100.0000 73.6587 97.9767 100.0000 90.3132 60.6512 100.0000 74.6639 100.1718 100.0000 91.1293 63.7484 100.0000 75.6648 102.3669 100.0000 91.9369 66.8457 100.0000 76.6571 104.5621 100.0000 92.7316 69.9472 100.0000 77.6494 106.7658 100.0000 93.5135 73.0530 100.0000 78.6331 108.9652 100.0000 94.2867 76.1588 100.0000 79.6125 111.1732 100.0000 95.0513 79.2689 100.0000 80.5919 113.3769 100.0000 95.8031 82.3790 100.0000 81.5671 115.5849 100.0000 96.5505 85.4934 100.0000 82.5379 117.7929 100.0000 97.2851 88.6121 100.0000 83.5044 120.0052 100.0000 98.0068 91.7307 100.0000 84.4753 122.2174 100.0000 98.7242 94.8494 100.0000 85.4418 124.4254 100.0000 99.4330 97.9724 100.0000 86.4041 126.6377 100.0000 100.1332 101.0997 100.0000 87.3706 128.8500 100.0000 100.8205 104.2270 100.0000 88.3414 131.0623 100.0000 101.5035 107.3543 100.0000 89.3080 133.2746 100.0000 102.1779 110.4858 100.0000 90.2788 135.4826 100.0000 102.8438 113.6174 100.0000 91.2496 137.6906 100.0000 103.5010 116.7490 100.0000 92.2248 139.8986 100.0000 104.1497 119.8849 100.0000 93.2042 142.1066 100.0000 104.7940 123.0207 100.0000 94.1879 144.3103 100.0000 105.4298 126.1566 100.0000 95.1716 146.5140 100.0000 106.0613 129.2968 100.0000 96.1553 148.7177 100.0000 106.6798 132.4370 100.0000 97.1433 150.9214 100.0000 107.2941 135.5814 100.0000 98.1314 153.1208 100.0000 107.8998 138.7259 100.0000 99.1194 155.3245 100.0000 108.5012 141.8704 100.0000 100.0988 157.5282 100.0000 109.0940 145.0148 100.0000 101.0782 159.7362 100.0000 109.6868 148.1636 100.0000 102.0534 161.9442 100.0000 110.2754 151.3080 100.0000 103.0156 164.1565 100.0000 110.8725 154.4568 100.0000 103.9649 166.3774 100.0000 111.4782 157.5970 100.0000 104.9057 168.5983 100.0000 112.0967 160.7414 100.0000 105.8293 170.8278 100.0000 112.7325 163.8773 100.0000 106.7357 173.0659 100.0000 113.3983 167.0089 100.0000 107.6292 175.3082 100.0000 114.1028 170.1319 100.0000 108.5055 177.5592 100.0000 114.8374 173.2463 100.0000 109.3733 179.8144 100.0000 115.6063 176.3521 100.0000 110.2453 182.0654 100.0000 116.3882 179.4579 100.0000 111.1259 184.3120 100.0000 117.1442 182.5680 100.0000 112.0366 186.5501 100.0000 117.8487 185.6910 100.0000 112.9817 188.7710 100.0000 118.5059 188.8225 100.0000 113.9697 190.9704 100.0000 119.1546 191.9498 100.0000 114.9491 193.1784 100.0000 119.6529 195.1115 100.0000 115.8684 195.4122 100.0000 117.6382 196.9286 100.0000 117.6382 196.9286 100.0000

It will also be appreciated that the airfoil 52 disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs using uniform geometric scaling. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z coordinate values of Table I, with the X, Y and Z non-dimensional coordinate values converted to inches, multiplied or divided by the same constant number.

An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table I. The actual profile on a manufactured turbine nozzle will be different than those in Table I, and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or −5% profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. It provides a unique profile to achieve 1) interaction among other stages in the turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings. The disclosed loci of points defined in Table I allow the gas turbine 12 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil 52 may be adopted as long as 1) interaction among other stages in the pressure turbine 10; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings are maintained in the scaled turbine.

The airfoil 52 described herein thus improves overall gas turbine 12 efficiency. Specifically, the airfoil 52 provides a desired turbine efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 52 also meets all aeromechanic and stress requirements. The turbine nozzle 50 described herein has very specific aerodynamic design requirements such as an upstream bucket radial back pressure (i.e., work splits) and radial velocity triangles for the downstream turbine rotors 150, 250, 350 and 450. Significant cross-functional design effort was required to meet these design goals. The airfoil 52 of the turbine nozzle 50 thus is of a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost-effective manner.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims or if they include equivalent structural elements with insubstantial differences from the literal language of the claims. 

What is claimed is:
 1. A turbine nozzle comprising an airfoil shape, the airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
 2. The turbine nozzle of claim 1, wherein the turbine nozzle forms part of a stage of a turbine.
 3. The turbine nozzle of claim 1, wherein the turbine nozzle is a first stage turbine nozzle.
 4. The turbine nozzle of claim 1, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 5. The turbine nozzle of claim 1, wherein a height of the turbine nozzle is about 2 inches to about 50 inches.
 6. The turbine nozzle of claim 1, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 7. A turbine nozzle comprising an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 8. The turbine nozzle of claim 7, wherein the turbine nozzle forms part of a stage of a turbine.
 9. The turbine nozzle of claim 7, wherein the turbine nozzle is a first stage turbine nozzle.
 10. The turbine nozzle of claim 7, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 11. The turbine nozzle of claim 7, wherein a height of the turbine nozzle is about 2 inches to about 50 inches.
 12. A turbine comprising a plurality of turbine nozzles, each of the turbine nozzles comprising an airfoil having an airfoil shape, the airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
 13. The turbine of claim 12, wherein the plurality of turbine nozzles forms part of a stage of a turbine.
 14. The turbine of claim 12, wherein the plurality of turbine nozzles comprises a plurality of first stage turbine nozzles.
 15. The turbine of claim 12, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 16. The turbine of claim 12, wherein a height of the turbine nozzle is about 2 inches to about 50 inches.
 17. The turbine of claim 12, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 18. The turbine of claim 12, wherein X represents a distance parallel to a turbine axis of rotation. 